Analytical Solutions for Transport Processes - Fluid Mechanics, Heat and Mass Transfer

Preface

Acknowledgements

Contents

Acronyms

Part I Fluid Mechanics

1 The Equations of Change in Fluid Mechanics and Their Analytical Solutions

1.1 The Equations of Change in Fluid Mechanics

1.2 Exact Solutions of the Equations of Change

1.2.1 Hydraulically Developed Flow

1.2.2 Further Exact Solutions

1.3 Approaches by Solving Simplified Equations of Change

1.3.1 Slender Flow Fields with Negligible Inertial Influence---The Lubrication Approximation

1.3.2 Slender Flow Fields at High Reynolds Number---The Boundary-Layer Approximation

1.3.3 Quasi One-Dimensional Flow

1.3.4 Quasi One-Dimensional Flow in a Slender Liquid Jet

1.3.5 Quasi One-Dimensional Flow in a Boundary Layer

References

2 The Equation for the Stokesian Stream Function and Its Solutions

2.1 The Equation for the Stream Function in Cartesian Coordinates

2.1.1 Linear, Unsteady Flow

2.1.2 Linear, Steady Flow

2.1.3 Nonlinear, Steady Flow with Constant Pressure

2.2 The Equation for the Stream Function in Cylindrical Coordinates

2.2.1 Polar, Linear, Unsteady Flow

2.2.2 Polar, Linear, Steady Flow

2.2.3 Polar, Nonlinear, Steady Flow

2.2.4 Axisymmetric, Linear, Unsteady Flow

2.2.5 Axisymmetric, Linear, Steady Flow

2.2.6 Axisymmetric, Nonlinear, Steady Flow with Constant Pressure

2.3 The Equation for the Stream Function in Spherical Coordinates

2.3.1 Linear, Unsteady Flow

2.3.2 Linear, Steady Flow

2.3.3 Nonlinear, Steady Flow with Constant Pressure

References

3 Laminar Two-Dimensional Flow

3.1 Steady Flow

3.1.1 Channel and Pipe Flows

3.1.2 Flow Between Coaxial Spinning Cylinders

3.1.3 Flow Outside a Spinning Sphere

3.1.4 Duct Flow with Injection and Suction Through the Walls

3.2 Unsteady Flow

3.2.1 The Two Stokesian Problems

3.2.2 Flow Outside a Cylinder in Oscillatory Spinning Motion

3.2.3 Starting and Fading Plane Couette Flow

3.2.4 Starting and Fading Channel and Pipe Flows

3.2.5 Pulsating Pipe Flow

3.2.6 Onset of Flow Between Two Concentric Spherical Shells

References

4 Lubrication Flow

4.1 Lubrication Approximation

4.2 Plane Slide Bearing

4.3 Pressure-Driven Flow Through a Plane Gap

4.4 Cylindrical Bearing

4.5 Pressure-Driven Flow Through a Cylindrical Gap

4.6 Pressure-Driven Flow Through a Spherical Gap

4.7 Wire Coating---Extended Lubrication Theory

References

5 Boundary-Layer Flow

5.1 Laminar Flow Along a Flat Plate

5.2 Flow Along a Slender Body of Revolution

5.3 Plane Submerged Free Jet

5.4 Axisymmetric Submerged Free Jet

5.5 Plane Free Shear Layer

5.6 Wake Behind a Flat Plate

References

6 Flows with Interfaces

6.1 Linear Temporal Instability of a Plane Liquid Sheet

6.2 Linear Temporal Capillary Instability of a Liquid Jet

6.3 Linear Spatial Capillary Instability of a Liquid Jet

6.4 Linear Oscillations of Drops and Bubbles

6.4.1 Linear Shape Oscillations of a Viscoelastic Drop

6.4.2 Linear Shape Oscillations of a Bubble in a Viscoelastic Liquid

6.5 Liquid Films from Drop Impact on Solid Substrates

6.6 Steady Creeping Flow Around a Spherical Particle

6.6.1 Hadamard--Rybczynski Flow Around a Fluid Spherical Particle

6.6.2 Stokes Flow Around a Solid Spherical Particle

References

Part II Heat and Mass Transfer

7 The Equations of Change for Heat and Mass Transfer and Their Analytical Solutions

7.1 The Thermal Energy Equation

7.2 Concepts for Simplifying the Thermal Energy Equation

7.3 The Equations of Change for Mass Transport

7.3.1 The Description of Fluid Mixtures

7.3.2 The Continuity Equation for a Mixture Component

7.4 Concepts for Simplifying the Continuity Equations

References

8 Heat Transfer

8.1 Heat Conduction

8.1.1 Steady Heat Conduction

8.1.2 Unsteady Heat Conduction---Early After Start or in Infinite Systems

8.1.3 Unsteady Heat Conduction---Long After Start in Finite Systems

8.2 Heat Transfer with Lumped Capacitances of Simple Geometries

8.3 Convective Heat Transport---Forced Convection

8.3.1 Heat Transfer Across a Flat-Plate Surface in Parallel Flow

8.3.2 Laminar Pipe Flow with Heat Transfer

8.4 Convective Heat Transport---Natural Convection

8.4.1 Natural Convection Along a Vertical Flat Plate

8.4.2 Natural Convection Between Two Vertical Flat Plates

References

9 Mass Transfer

9.1 Steady Diffusive Mass Transport---Equimolar and Stefan Flow

9.2 Diffusive Transfer Across Spherical, Spheroidal and Hyperboloidal Interfaces

9.2.1 Introduction

9.2.2 The Sherwood Number of Equimolar Diffusion for a Sphere

9.2.3 The Sherwood Number of Equimolar Diffusion on Spheroidal and Hyperboloidal Surfaces

9.3 Convective Mass Transfer from Flat Plate Surfaces

9.4 Liquid Phase Analysis in the Convective Drying of Drops

9.4.1 Introduction

9.4.2 Mathematical Description

9.4.3 Definition of the Problem

9.4.4 Analytical Solution of the Problem

9.4.5 Evaluation of the Equations and Example Calculations

References

Part IIIAppendices

Appendix AThe Equations of Change in TransportProcesses

Appendix BBasic Vector Analytical Operations

Appendix CSpecial Functions of Mathematical Physics

Index